On LAM's and SAM's for Halley's rotation

Non principal axis rotation for comet Halley is inferred from dual periodicities evident in the observations. The modes where the spin axis precesses around the axis of minimum moment of inertia (long axis mode or LAM) and where it precesses around the axis of maximum moment of inertia (short axis mode or SAM) are described from an inertial point of view. The currently favored LAM model for Halley's rotation state satisfies observational and dynamical constraints that apparently no SAM can satisfy. But it cannot reproduce the observed post perihelion brightening through seasonal illumination of localized sources on the nucleus, whereas a SAM can easily produce post or pre perihelion brightening by this mechanism. However, the likelihood of a LAM rotation for elongated nuclei of periodic comets such as Halley together with Halley's extreme post perihelion behavior far from the Sun suggest that Halley's post perihelion brightening may be due to effects other than seasonal illumination of localized sources, and therefore such brightening may not constrain its rotation state

The production of braids in Saturn's F ring

The braided structure noted in Voyager images of the Saturn F ring is presently addressed by two models. In the first, the pattern is generated by a narrow and initially uniform ring's passing of a nearby satellite, followed by an embedded moonlet gravitational acceleration-induced doubling back so that trajectories of the ring particles traverse one end of the classic horseshoe orbit. In the second model, the F ring is composed of two separated strands before the Moon's passage, so that a long braided pattern can be generated by the subsequent drift in relative phase; the embedded moonlet is thereby obviated

Mercury's Internal Structure

We describe the current state of knowledge about Mercury's interior structure. We review the available observational constraints, including mass, size, density, gravity field, spin state, composition, and tidal response. These data enable the construction of models that represent the distribution of mass inside Mercury. In particular, we infer radial profiles of the pressure, density, and gravity in the core, mantle, and crust. We also examine Mercury's rotational dynamics and the influence of an inner core on the spin state and the determination of the moment of inertia. Finally, we discuss the wide-ranging implications of Mercury's internal structure on its thermal evolution, surface geology, capture in a unique spin-orbit resonance, and magnetic field generation.Comment: 36 pages, 11 figures, in press, to appear in "Mercury - The View after MESSENGER", S. C. Solomon, B. J. Anderson, L. R. Nittler (editors), Cambridge University Pres

Effect of core--mantle and tidal torques on Mercury's spin axis orientation

The rotational evolution of Mercury's mantle and its core under conservative and dissipative torques is important for understanding the planet's spin state. Dissipation results from tides and viscous, magnetic and topographic core--mantle interactions. The dissipative core--mantle torques take the system to an equilibrium state wherein both spins are fixed in the frame precessing with the orbit, and in which the mantle and core are differentially rotating. This equilibrium exhibits a mantle spin axis that is offset from the Cassini state by larger amounts for weaker core--mantle coupling for all three dissipative core--mantle coupling mechanisms, and the spin axis of the core is separated farther from that of the mantle, leading to larger differential rotation. The relatively strong core--mantle coupling necessary to bring the mantle spin axis to its observed position close to the Cassini state is not obtained by any of the three dissipative core--mantle coupling mechanisms. For a hydrostatic ellipsoidal core--mantle boundary, pressure coupling dominates the dissipative effects on the mantle and core positions, and dissipation together with pressure coupling brings the mantle spin solidly to the Cassini state. The core spin goes to a position displaced from that of the mantle by about 3.55 arcmin nearly in the plane containing the Cassini state. With the maximum viscosity considered of $\nu\sim 15.0\,{\rm cm^2/s}$ if the coupling is by the circulation through an Ekman boundary layer or $\nu\sim 8.75\times 10^5\,{\rm cm^2/s}$ for purely viscous coupling, the core spin lags the precessing Cassini plane by 23 arcsec, whereas the mantle spin lags by only 0.055 arcsec. Larger, non hydrostatic values of the CMB ellipticity also result in the mantle spin at the Cassini state, but the core spin is moved closer to the mantle spin.Comment: 35 pages, 7 figure

Mercury's Internal Structure

We describe the current state of knowledge about Mercury's interior structure. We review the available observationalconstraints, including mass, size, density, gravity eld, spin state, composition, and tidal response. These data enablethe construction of models that represent the distribution of mass inside Mercury. In particular, we infer radial prolesof the pressure, density, and gravity in the core, mantle, and crust. We also examine Mercury's rotational dynamicsand the inuence of an inner core on the spin state and the determination of the moment of inertia. Finally, we discussthe wide-ranging implications of Mercury's internal structure on its thermal evolution, surface geology, capture in aunique spin-orbit resonance, and magnetic eld generation

First MESSENGER orbital observations of Mercury's librations

We have coregistered laser altimeter profiles from 3 years of MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) orbital observations with stereo digital terrain models to infer the rotation parameters for the planet Mercury. In particular, we provide the first observations of Mercury's librations from orbit. We have also confirmed available estimates for the orientation of the spin axis and the mean rotation rate of the planet. We find a large libration amplitude of 38.9 ± 1.3 arc sec and an obliquity of the spin axis of 2.029 ± 0.085 arc min, results confirming that Mercury possesses a liquid outer core. The mean rotation rate is observed to be (6.13851804 ± 9.4 × 10−7)°/d (a spin period of 58.6460768 days ± 0.78 s), significantly higher than the expected resonant rotation rate. As a possible explanation we suggest that Mercury is undergoing long‐period librational motion, related to planetary perturbations of its orbit

Mercury's Moment of Inertia from Spin and Gravity Data

Earth-based radar observations of the spin state of Mercury at 35 epochs between 2002 and 2012 reveal that its spin axis is tilted by (2.04 plus or minus 0.08) arc min with respect to the orbit normal. The direction of the tilt suggests that Mercury is in or near a Cassini state. Observed rotation rate variations clearly exhibit an 88-day libration pattern which is due to solar gravitational torques acting on the asymmetrically shaped planet. The amplitude of the forced libration, (38.5 plus or minus 1.6) arc sec, corresponds to a longitudinal displacement of ∼450 m at the equator. Combining these measurements of the spin properties with second-degree gravitational harmonics (Smith et al., 2012) provides an estimate of the polar moment of inertia of MercuryC/MR2 = 0.346 plus or minus 0.014, where M and R are Mercury's mass and radius. The fraction of the moment that corresponds to the outer librating shell, which can be used to estimate the size of the core, is Cm/C = 0.431 plus or minus 0.025

Tidal Evolution of Close-in Planets

Recent discoveries of several transiting planets with clearly non-zero eccentricities and some large inclinations started changing the simple picture of close-in planets having circular and well-aligned orbits. Two major scenarios to form such planets are planet migration in a disk, and planet--planet interactions combined with tidal dissipation. The former scenario can naturally produce a circular and low-obliquity orbit, while the latter implicitly assumes an initially highly eccentric and possibly high-obliquity orbit, which are then circularized and aligned via tidal dissipation. We investigate the tidal evolution of transiting planets on eccentric orbits. We show that the current and future orbital evolution of these systems is likely dominated by tidal dissipation, and not by a more distant companion. Although most of these close-in planets experience orbital decay all the way to the Roche limit, there are two characteristic evolution paths for them, depending on the relative efficiency of tidal dissipation inside the star and the planet. We point out that the current observations may be consistent with one of them. Our results suggest that at least some of the close-in planets with non-zero orbital eccentricity may have been formed by tidally circularizing an initially eccentric orbit. We also find that even when the stellar spin-orbit misalignment is observed to be small at present, some systems could have had a highly misaligned orbit in the past. Finally, we also re-examine the recent claim by Levrard et. al., who found that all orbital and spin parameters evolve on a similar timescale to orbital decay.Comment: Accepted for publication in ApJ, 22 pages, 19 figures, 2 tables, Corrupted figures are fixe

The low‐degree shape of Mercury

The shape of Mercury, particularly when combined with its geoid, provides clues to the planet's internal structure, thermal evolution, and rotational history. Elevation measurements of the northern hemisphere acquired by the Mercury Laser Altimeter on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft, combined with 378 occultations of radio signals from the spacecraft in the planet's southern hemisphere, reveal the low‐degree shape of Mercury. Mercury's mean radius is 2439.36 ± 0.02 km, and there is a 0.14 km offset between the planet's centers of mass and figure. Mercury is oblate, with a polar radius 1.65 km less than the mean equatorial radius. The difference between the semimajor and semiminor equatorial axes is 1.25 km, with the long axis oriented 15° west of Mercury's dynamically defined principal axis. Mercury's geoid is also oblate and elongated, but it deviates from a sphere by a factor of 10 less than Mercury's shape, implying compensation of elevation variations on a global scale